... Other mechanical timepieces are in your collection? I am curious because I, too, consider myself to have a smallish collection of watches. But you know what they say, quality not quantity. Case in point: Jaeger LeCoultre. For you and me (and many others, including the other respondent to your post) Jaeger LeCoultre represents the pinnacle of watchmaking. Our AMVOX watches are fairly sophisticated pieces of horology - on mine the chronograph functions are actuated by pressing the crystal at 12:00 and 6:00 - and, as I was recently informed, AMVOX watches are more "concept" than "practical". I suppose if you drive a very sophisticated car (Aston Martin, for lack of a better example), it's going to need to be at the spa more often than say, an Audi A7. For some reason we just think it's okay if it happens to be our car as opposed to one of our watches. This is not to say that it's okay for someone's AM to be in the shop without rhyme or reason, but I can say that none of my other JLC's have had the kind of issues the AMVOX had when I first purchased it.
Believe me, if it is costing you $1,000 for the watch to be serviced in, of all places, Le Sentier, then you are getting off light. By all means, have that watch serviced! My guess is it was a bit older than the original AD disclosed when originally purchased. Or, unbeknownst to you, the watch may have fallen down or been struck in some way that has caused this issue. Nevertheless, fact of the matter is that even having a display back would probably offer no clue into why the watch is not functioning as necessary. From my experience, could be something as simple as a hair (human or not) that somehow got through the case and into the movement.